Skip to main content

The Quantum Potential in Particle and Field Theory Models

  • Chapter
  • First Online:
Quantum Potential: Physics, Geometry and Algebra

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

  • 1329 Accesses

Abstract

As known, the Klein-Gordon equation describe the behaviour of relativistic spinless particles.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Holland, P.R.: Geometry of dislocated de Broglie waves. Found. Phys. 17(4), 345–363 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  2. Shojai, A., Shojai, F.: About some problems raised by the relativistic form of de Broglie-Bohm theory of pilot wave. Phys. Scr. 64(5), 413–416 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Shojai, F., Shojai, A.: Understanding quantum theory in terms of geometry. arXiv:gr-qc/0404102 v1 (2004)

    Google Scholar 

  4. Bertoldi, G., Faraggi, A., Matone, M.: Equivalence principle, higher dimensional Moebius group and the hidden antisymmetric tensor of quantum mechanics. Class. Quantum Grav. 17, 3965 (2000)

    Google Scholar 

  5. Brown, H., Sjöqvist, E., Bacciagaluppi, G.: Remarks on identical particles in de Broglie-Bohm theory. Phys. Lett. A 251, 229–235 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Brown, H.: The quantum potential: the breakdown of classical sympletic symmetry and the energy of localisation and dispersion. arXiv:quant-ph/9703007 (1997)

    Google Scholar 

  7. Brown, H., Holland, P.: Simple applications of Noether’s first theorem in quantum mechanics and electromagnetism. Am. J. Phys. 72(1), 34 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. Dewdney, C., Horton, G.: Relativistically invariant extension of the de Broglie-Bohm theory of quantum mechanics. J. Phys. A: Math. Gen. 35(47), 10117 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Holland, P.R.: New trajectory interpretation of quantum mechanics. Found. Phys. 38, 881–911 (1998)

    Article  MathSciNet  Google Scholar 

  10. Holland, P.R.: Hamiltonian theory of wave and particle in quantum mechanics I: Liouville’s theorem and the interpretation of the de Broglie-Bohm theory. Nuovo Cimento B 116, 1043–1070; Hamiltonian theory of wave and particle in quantum mechanics II: Hamilton-Jacobi theory and particle back-reaction. Nuovo Cimento B 116, 1143–1172 (2001)

    Google Scholar 

  11. Holland, P.R.: Causal interpretation of Fermi fields. Phys. Lett. A 128, 9–18 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  12. Holland, P.R.: Uniqueness of conserved currents in quantum mechanics. Ann. Phys. 12(7/8), 446–462 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Holland, P.R.: The de Broglie-Bohm theory of motion and quantum field theory. Phys. Rep. 224(3), 95–150 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  14. Holland, P.R.: Implications of Lorentz covariance for the guidance equation in two-slit quantum interference. Phys. Rev. A 67, 062105 (2003)

    Article  ADS  Google Scholar 

  15. Holland, P.R.: Computing the wavefunction from trajectories: particle and wave pictures in quantum mechanics and their relation. Ann. Phys. 315(2), 505–531 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Holland, P.R.: Constructing the electromagnetic field from hydrodynamic trajectories. Proc. R. Soc. A 461, 3659–3679 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Horton, G., Dewdney, C.: A non-local, Lorentz-invariant, hidden variable interpretation of relativistic quantum mechanics based on particle trajectories. J. Phys. A: Math. Gen. 34, 9871 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Horton, G., Dewdney, C.: A relativistically covariant version of Bohm’s quantum field theory for the scalar field. J. Phys. A: Math. Gen. 37, 11935 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Horton, G., Dewdney, C., Ne’eman, U.: de Broglie’s pilot-wave theory for the Klein–Gordon equation and its space-time pathologies. Found. Phys. 32(3), 463–476 (2002)

    Article  MathSciNet  Google Scholar 

  20. Horton, G., Dewdney, C., Nesteruk, A.: Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation. J. Phys. A: Math. Gen. 33, 7337 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Mostafazadeh, A., Zamani, F.: Conserved current densities, localisation probabilities, and a new global gauge symmetry of Klein-Gordon fields. arXiv:quant-ph/0312078 (2003)

    Google Scholar 

  22. Mostafazadeh, A.: Quantum mechanics of Klein-Gordon-type fields and quantum cosmology. Ann. Phys. 309(1), 1–48 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  23. Carroll, R.: Quantum Theory, Deformation, and Integrability. North-Holland, Amsterdam (2000)

    MATH  Google Scholar 

  24. Carroll, R.: Integrable systems as quantum mechanics. arXiv:quant-ph/0309159 (2003)

    Google Scholar 

  25. Carroll, R.: (X, ψ) duality and enhanced dKdV on a riemann surface. Nucl. Phys. B 502(3), 561–593 (1997)

    Article  ADS  MATH  Google Scholar 

  26. Carroll, R.: On the whitham equations and (X, ψ) duality. Supersymmetry and integrable models. lecture notes in physics vol. 502, pp. 33–56. Springer lecture notes in physics (1998)

    Google Scholar 

  27. Faraggi, A., Matone, M.: The equivalence postulate of quantum mechanics. Int. J. Mod. Phys. A 15, 1869–2017 (2000)

    MathSciNet  ADS  MATH  Google Scholar 

  28. Matone, M.: The cocycle of quantum Hamilton-Jacobi equation and the stress tensor of CFT. Brazilian. J. Phys. 35(02A), 316–327 (2005)

    Google Scholar 

  29. Nikolic, H.: Covariant canonical quantization of fields and Bohmian mechanics. Eur. Phys. J. C 42(3), 365 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. Nikolic, H.: Bohmian particle trajectories in relativistic bosonic quantum field theory. Found. Phys. Lett. 17(4), 363–380 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  31. Nikolic, H.: Bohmian particle trajectories in relativistic fermionic quantum field. Found. Phys. Lett. 18(2), 123–138 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  32. Nikolic, H.: Quantum determinism from quantum general covariance. Int. J. Mod. Phys. D15(2006), 2171–2176 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  33. Bohm, D., Hiley, B.J.: On the relativistic invariance of a quantum theory based on beables. Found. Phys. 21(2), 243–250 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  34. Gull, S., Lasenby, A., Doran, C.: Electron paths, tunnelling and diffraction in the spacetime algebra. Found. Phys. 23(10), 1329–1356 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  35. Hiley, B.J., Callaghan, R.E.: The Clifford algebra approach to quantum mechanics B: the Dirac particle and its relation to the Bohm approach. arXiv:1011.4033v1 [math-ph] (2010)

    Google Scholar 

  36. Kaloyerou, P.N.: The causal interpretation of the electromagnetic field. Phys. Rep. 244(6), 287–358 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  37. Valentini, A.: Signal-locality, uncertainty, and the subquantum H-theorem. I. Phys. Lett. A 156, 5–11 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  38. Nikolic, H.: The general-covariant and gauge-invariant theory of quantum particles in classical backgrounds. Int. J. Mod. Phys. D 12(3), 407 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. Nikolic, H.: A general covariant concept of particles in curved background. Phys. Lett. B 527(1), 119–124 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Nikolic, H.: Erratum to: “a general covariant concept of particles in curved background”. Phys. Lett. B 529(3), 265 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  41. Nikolic, H.: There is no first quantization except in the de Broglie-Bohm interpretation. arXiv:quant-ph/0307179 (2003)

    Google Scholar 

  42. Nikolic, H.: Covariant many-fingered time Bohmian interpretation of quantum field theory. Phys. Lett. A348, 166–171 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  43. Nikolic, H.: Boson-fermion unification, superstrings, and Bohmian mechanics. Found. Phys. 39(10), 1109–1138 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ignazio Licata .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Author(s)

About this chapter

Cite this chapter

Licata, I., Fiscaletti, D. (2014). The Quantum Potential in Particle and Field Theory Models. In: Quantum Potential: Physics, Geometry and Algebra. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-00333-7_2

Download citation

Publish with us

Policies and ethics